Related papers: Spectral action on SU_q(2)
We study the spectrum of a periodic non-self-adjoint Dirac operator, and its dependence on a semiclassical parameter is also considered. Several bounds on the spectrum are obtained which provide sharp spectral enclosure estimates.…
Analytical expressions are given for the eigenvalues and eigenvectors of a Hamiltonian with su_q(2) dynamical symmetry. The relevance of such an operator in Quantum Optics is discussed. As an application, the ground state energy in the…
We study spectral triples over noncommutative principal U(1)-bundles of arbitrary dimension and formulate a compatibility condition between the connection and the Dirac operator on the total space and on the base space of the bundle.…
A Dirac operator D on the standard Podles sphere is defined and investigated. It yields a spectral triple such that |D|^{-z} is of trace class for Re z>0. Commutators with the Dirac operator give the distinguished 2-dimensional covariant…
We derive a number of spectral results for Dirac operators in geometrically nontrivial regions in $\mathbb{R}^2$ and $\mathbb{R}^3$ of tube or layer shapes with a zigzag type boundary using the corresponding properties of the Dirichlet…
Two years ago, we found the supersymmetric counterpart of the spectral triple which specified noncommutative geometry. Based on the triple, we derived gauge vector supermultiplets, Higgs supermultiplets of the minimum supersymmetric…
A supersymmetric theory in two-dimensions has enough data to define a noncommutative space thus making it possible to use all the tools of noncommutative geometry. In particular, we apply this to the N=1 supersymmetric non-linear sigma…
We explain the notion of minimality for an equivariant spectral triple and show that the triple for the quantum SU(2) group constructed by Chakraborty and Pal in \cite{c-p1} is minimal. We also give a decomposition of the spectral triple…
Continuing our study of spectral triples on quantum domains, we look at unbounded invariant and covariant derivations in the quantum annulus. In particular, we investigate whether such derivations can be implemented by operators with…
We construct a canonical geometrically realised Connes spectral triple or `Dirac operator' $D\!\!\!/$ from the data of a quantum metric $g\in \Omega^1\otimes_A\Omega^1$ and quantum Levi-Civita bimodule connection, at the pre-Hilbert space…
Operator angle-action variables are studied in the frame of the SU(2) algebra, and their eigenstates and coherent states are discussed. The quantum mechanical addition of action-angle variables is shown to lead to a novel non commutative…
The paper deals with the semi-Dirac operator in a half-space arising in the description of quasiparticles in quantum mechanics as well as in semi-metals materials and related structures. It completely shows the self-adjointness, computes…
Given $L$ a solvable Lie Algebra of operators acting on a Banach space $E$, we study the action of the opposite algebra of $L$, $L'$, on $E^*$. Moreover, we extend S{\l}odkowski joint spectra, $\sigma_{\delta,k}$, $\sigma_{\pi,k}$, and we…
We present examples of equivariant noncommutative Lorentzian spectral geometries. The equivariance with respect to a compact isometry group (or quantum group) allows to construct the algebraic data of a version of spectral triple geometry…
We extend naturally the spectral triple which define noncommutative geometry (NCG) in order to incorporate supersymmetry and obtain supersymmetric Dirac operator D_M which acts on Minkowskian manifold. Inversely, we can consider the…
We give a derivation of the Dirac operator on the noncommutative $2$-sphere within the framework of the bosonic fuzzy sphere and define Connes' triple. It turns out that there are two different types of spectra of the Dirac operator and…
We construct a family of self-adjoint operators D_N which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space CP_q(l), for any l>1 and 0<q<1. They provide 0^+ dimensional equivariant…
In this paper, we study the spectrality of the non-self-adjoint Dirac operator L(Q) with a complex-valued periodic matrix potential Q. We establish a condition on the off-diagonal elements of the matrix Q under which L(Q) is an…
We propose a construction for spectral triple on algebras associated with subshifts. One-dimensional subshifts provide concrete examples Z-actions on Cantor sets. The C*-algebra of this dynamical system is generated by functions in C(X) and…
Approximating the sum over all gauge field configurations in the QCD partition function by a liquid of instantons, we calculate the spectrum of the Dirac operator for two and three colors and for 0, 1 and 2 flavors. We find a remarkable…